How do you find the exact value of arccos(sin(pi/3))?

2 Answers
Oct 6, 2016

pi/6

Explanation:

knowing that sin(pi/3)=sqrt3/2
" "
arccos(sin(pi/3))=arccos((sqrt3)/2)
" "
we know that cos(pi/6)=sqrt3/2
" "
so, pi/6=arccos(sqrt3/2)
" "
arccos(sin(pi/3))=arccos((sqrt3)/2)=pi/6

Nov 6, 2017

arccos(sin(1/3pi))=1/6pi

Explanation:

By definition, cos(1/2pi-theta)=sintheta for all theta

therefore arccos (sin(1/3pi))=arccos (cos(1/2pi-1/3pi))=arccos (cos (1/6pi))=1/6pi